Relation between Laplacian and conductivity computation step

Current interpretation:
>Every pixel in the source is transformed into 9 pixels, with surrounding pixels being difference in that direction and the pixel itself is replaced by zero. Then kernel is computed for each pixel using conductivity function, convolved with the new 9 pixels, and then convolved by Laplacian kernel. This is the only explanation I have come up with that does the same as the implementation.

So the question is "Is this right interpreation?"

The original wording of the algorithm can be found here:
http://www.sci.utah.edu/~gerig/CS7960-S2010/materials/Perona-Malik/anisotropic_diffusion-Book.pdf